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Computing Walrasian Equilibria: Fast Algorithms and Structural Properties
[article]

2016
*
arXiv
*
pre-print

We present the first polynomial time

arXiv:1511.04032v2
fatcat:tharcfrx65b4xnr7y4nonpxuei
*algorithm*for*computing**Walrasian*equilibrium in an economy with indivisible goods*and*general buyer valuations having only access to an aggregate demand oracle, i.e ... We also give the fastest known*algorithm*for*computing**Walrasian*equilibrium for gross substitute valuations in the value oracle model. ... Murota*and*Tamura [MT03] give combinatorial*algorithms*for the problem of*computing**Walrasian**equilibria*via a reduction to the M -convex submodular flow problem. ...##
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Computing Walrasian equilibria: fast algorithms and structural properties

2018
*
Mathematical programming
*

We present the first polynomial time

doi:10.1007/s10107-018-1334-9
fatcat:fytimwept5dejbxc4i5qvvpk4e
*algorithm*for*computing**Walrasian*equilibrium in an economy with indivisible goods*and*general buyer valuations having only access to an aggregate demand oracle, i.e ... We also give the fastest known*algorithm*for*computing**Walrasian*equilibrium for gross substitute valuations in the value oracle model. ... Comparison to related work Iterative auctions*and*subgradient*algorithms*The first*algorithm*for*computing**Walrasian**equilibria*in an economy of indivisible goods is due to Kelso*and*Crawford [21]*and*...##
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Solving Deterministic and Stochastic Equilibrium Problems via Augmented Walrasian

2017
*
Computational Economics
*

We described a method to solve deterministic

doi:10.1007/s10614-017-9733-1
fatcat:g5okmtfpc5eunnxsa2wjwkcdua
*and*stochastic Walras equilibrium models based on associating with the given problem a bifunction whose maxinf-points turn out to be equilibrium points. ... In the dynamic versions of our models, deterministic*and*stochastic, we are mostly concerned with models that equip the agents with a mechanism to transfer goods from one time period to the next, possibly ... We thank David Woodruff, University of California Davis, for his assistance with Pyomo, the optimization modeling language used in the*computational*implementation of our*algorithm*. ...##
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Approximation of Walrasian equilibrium in single-minded auctions

2005
*
Theoretical Computer Science
*

We show NP-hardness of the optimization problem, establish lower

doi:10.1016/j.tcs.2005.03.008
fatcat:66rb3hdqfjdtdbphsqnu4m6fbi
*and*upper bounds of R, as well as develop greedy*algorithms*to approximate the optimal value of R. ... We consider a social optimization model of pricing scheme in single-minded auctions, in cases where*Walrasian*equilibrium does not exist. ... [3] developed a*fast**algorithm*to achieve the equilibrium for the cases with nice*structures**and*proved the NP-hardness for the general case. ...##
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On Approximate Welfare- and Revenue-Maximizing Equilibria for Size-Interchangeable Bidders
[article]

2017
*
arXiv
*
pre-print

In a

arXiv:1708.03097v1
fatcat:ml5l7ake4raz3hyrwtni4a6nt4
*Walrasian*equilibrium (WE), all bidders are envy-free (EF), meaning that their allocation maximizes their utility;*and*the market clears (MC), meaning that the price of unallocated goods is zero. ... Instead of*computing*an outcome that simultaneously yields an allocation*and*corresponding prices, one could first solve for an allocation that respects a reserve price,*and*then solve for a corresponding ... paves the way for*fast**computational*methods to nd such outcomes. ...##
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A global Newton method to compute Nash equilibria

2003
*
Journal of Economic Theory
*

A new

doi:10.1016/s0022-0531(03)00005-x
fatcat:fimnz7mftrbltc6tkwuqvgqvgi
*algorithm*is presented for*computing*Nash*equilibria*of¯nite games. ... The*algorithm*is outlined*and**computational*experience is reported. JEL Classi¯cation C63. ... games (RosenmÄ uller, 1971 ; Wilson, 1971) ,*and*applications to*Walrasian**equilibria*of economic models (Balasko, 1988; Eaves*and*Schmedders, 1999 ,*and*their extensive references; Scarf*and*Hansen ...##
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Chapter 38 Computation and multiplicity of equilibria
[chapter]

1991
*
Handbook of Mathematical Economics
*

Thus, if we had an

doi:10.1016/s1573-4382(05)80013-x
fatcat:as5rsx26m5eedpwczmg36ninmu
*algorithm*for*computing**equilibria*of arbitrary economies specified in terms of preferences*and*endowments, using it to*compute*fixed points would be complicated. ... A simple extension of our previous argument demonstrates the existence of equilibrium in a production technology*and*suggests*algorithms*for*computing**equilibria*. ...##
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The Price is (Probably) Right: Learning Market Equilibria from Samples
[article]

2021
*
arXiv
*
pre-print

We consider the setting where player valuations are unknown; using a PAC learning-theoretic framework, we analyze some classes of common valuation functions,

arXiv:2012.14838v2
fatcat:fw6thtnmurad5jfn5a73d2xree
*and*provide*algorithms*which output direct ... Equilibrium*computation*in markets usually considers settings where player valuation functions are known. ... Brânzei et al. (2016) present an*Algorithm*to*compute**equilibria*under equal budgets. We extend this*Algorithm*to settings where each player has a unique budget. Theorem 5.2. ...##
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A Hydraulic Approach to Equilibria of Resource Selection Games
[article]

2016
*
arXiv
*
pre-print

., asymmetric singleton congestion games) with nonatomic players, the coincidence of strong

arXiv:1403.7605v7
fatcat:eaitof23braozhlavgdc34erve
*equilibria**and*Nash*equilibria*in such games,*and*the uniqueness of the cost of each given resource across all ... -dependent weighting, is defined,*and*the results are extended to this family, showing the existence of strong*equilibria*,*and*showing that while resource costs are no longer unique across Nash*equilibria*... the*structure*of the input, this may render the complexity of this*computation*exponential in the encoded input size. ...##
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A Consumer-Theoretic Characterization of Fisher Market Equilibria
[article]

2022
*
arXiv
*
pre-print

The main tools we use are the dual concepts of expenditure minimization

arXiv:2107.08153v2
fatcat:ic3xhujysvdtlfmbnwi4ltgxsq
*and*indirect utility maximization. ... We then prove that the subdifferential of the dual of our convex program is equal to the negative excess demand in the associated market, which makes generalized gradient descent equivalent to*computing*... A detailed inquiry into the*computational**properties*of market*equilibria*was initiated by Devanur et al. ...##
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A Hydraulic Approach to Equilibria of Resource Selection Games

2016
*
Proceedings of the 2016 ACM Conference on Economics and Computation - EC '16
*

., asymmetric singleton congestion games) with nonatomic players, the coincidence of strong

doi:10.1145/2940716.2940749
dblp:conf/sigecom/GonczarowskiT16
fatcat:qczyferbgnbhjf2xi5hiqn3nvu
*equilibria**and*Nash*equilibria*in such games,*and*the uniqueness of the cost of each given resource across all ... ,*and*showing that while resource costs are no longer unique across Nash*equilibria*in games of this family, they are nonetheless unique across all strong Nash*equilibria*, drawing a novel fundamental connection ... the*structure*of the input, this may render the complexity of this*computation*exponential in the encoded input size. ...##
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The Complexity of Exchange*

2005
*
Economic Journal
*

Recent results on the

doi:10.1111/j.1468-0297.2005.01001.x
fatcat:gxdo72yw2ffp5oabztktfjeglu
*computational*complexity are reviewed. The non-polynomial complexity of these*algorithms*makes*Walrasian*general equilibrium an implausible conception. ... The*computational*complexity of two classes of market mechanisms is compared. First the*Walrasian*interpretation in which prices are centrally*computed*by an auctioneer. ... In particular, k-lateral exchange*equilibria*have much better*computational*complexity than do*Walrasian**equilibria*. ...##
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Page 1608 of Mathematical Reviews Vol. , Issue 87c
[page]

1987
*
Mathematical Reviews
*

Preckel, Paul V. (1-PURD) 87c:90048 Alternative

*algorithms*for*computing*economic*equilibria*. Economic equilibrium: model formulation*and*solution. Math. Programming Stud. No. 23 (1985), 163-172. ... We demonstrate that if the probability that agents are linked with each other does not tend to zero too*fast*as this number increases, then the probability that a coalition will form*and*block any non-*Walrasian*...##
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Complexity Theory, Game Theory, and Economics: The Barbados Lectures
[article]

2019
*
arXiv
*
pre-print

It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication

arXiv:1801.00734v2
fatcat:r6sz7jskqjbs7gxof52fbjikom
*and**computational*complexity of*computing**equilibria*;*and*the Lunar Lectures, focusing on applications of complexity ... 19--23, 2017, as the 29th McGill Invitational Workshop on*Computational*Complexity. ... problem that is hard*and*yet*structured*enough to be solved using approximate Nash equilibrium*computation*. ...##
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Decoupling Markets and Individuals: Rational Expectations Equilibrium Outcomes from Information Dissemination Among Boundedly-Rational Traders

2012
*
Social Science Research Network
*

*structural*

*properties*of markets. ... These findings suggest that market

*structure*is an important determinant of efficient aggregate level outcomes,

*and*that care is necessary not to overstate the importance of human cognition

*and*conscious ... This control allows us to hold trader "cognition" constant at a specified level

*and*explore the outcome

*properties*of market

*structures*

*and*environment. ...

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